On integral equations of the first kind with logarithmic kernels
type: Item
instance of: scholarly article
title: On integral equations of the first kind with logarithmic kernels
zbMATH Open document ID: 0682.45001
DOI: 10.1216/JIE-1988-1-4-549
author: Y. Yan
author: Ian H. Sloan
published in: Journal of Integral Equations and Applications
publication date: 1988-01-01T00:00:00Z
review text: The authors give a detailed study on the existence and uniqueness of the solution for one-dimensional integral equations of the first kind with logarithmic kernels. The analysis is given for both closed and open contours, and existence and uniqueness theorems are established. The method of proof is based on the transfinite diameter or logarithmic capacity, and on function spaces associated with Fourier series expansions. The behavior of the solutions is also investigated for the case of polygonal contour, by means of a perturbation argument applied to the results for smooth closed curves.
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 4117190
zbMATH Keywords: integral equations of the first kind
zbMATH Keywords: logarithmic kernels
zbMATH Keywords: transfinite diameter
zbMATH Keywords: logarithmic capacity
zbMATH Keywords: Fourier series expansions
reviewed by: Jacob Burbea
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4117190